VARIATIONS (statement, constant of variation).pptx

It is a lesson in grade 9 for the second quarter

1. VARIATIONS Are instances in varying.

2. FOUR VARIATIONS DIRECT VARIATION INVERSE/INDIRECT VARIATION JOINT VARIATION COMBINED VARIATION

3. 1. DIRECT VARIATION takes place when a situation produces pair of numbers in which their ratio is constant .

4. (For two quantities as x and y) An increase in x causes an increase in y as well and vice versa.

5. Statements: y = kx w here k is the constant of variation . Math translation: “y varies directly as x” “y is directly proportional to x” “y is proportional to x”

6. Using his bicycle, Jericho travels a distance of 10km/ hr on a steep road. The table shows the distance he has travelled at a particular length of time. Time / t ( hr ) 1 2 3 4 5 Distance/ d (km) 10 20 30 40 50

7. The above situation shows that the ratio d/t for every pair of numbers are the same or constant , that is, = 10 or d = 10t  

8. Time / t ( hr ) 1 2 3 4 5 Distance/ d (km) 10 20 30 40 50

9. A direct variation may also relate four quantities in proportion (an equality of ratios) as or =  

10. Example1: If y varies directly as x and y = 24 and x = 6, find the constant of variation and the equation of variation.

11. y = kx 24 = 6k 24 =   k = 4 y = 4 x

12. Example2: Y varies directly as x, and y=32 when x=8. Find the constant of variation and find y when x=17.

13. y = kx 32 = 8k 32 =   k = 4 y = 68 y = 17(4)

14. Example3: If y varies directly as x and y is 100 when x is 4, what is y when x is 5?

15. y = kx 100 = 4 k 100 =   k = 25 y = 5 (25) y = 125